We evaluate the benefits of our approach by considering alternative strategies. First, we use the estimation method of [1]}, where the covariance matrix \( \tilde{\Sigma }\)  in (REF ) is estimated using the sample variance and the sample mean of the return series. We call this strategy Moment-SMV. Second, we evaluate the classic MV of [2]}. In this case, we model the conditional covariance of asset returns using several well-known autoregressive dynamics, i.e. the multivariate GARCH Dynamic Conditional Correlation model ([3]}), under both the multivariate Normal (MV-G-DCC-N) and Student-t (MV-G-DCC-t) error distributions, and the asymmetric Dynamic Conditional Correlation model with multivariate Normal (MV-G-aDCC-N) and Student-t (MV-G-aDCC-t) errors. Moreover, since the MV strategy could often be inadequate in controlling for asymmetric risk-averse agents, we also consider the above strategies under the multivariate skew Normal (SN) and the multivariate skew Student-t (St) distributions of [4]} as further competing strategies, which we denote by MV-G-DCC-SN, MV-G-DCC-St, MV-G-aDCC-SN and MV-G-aDCC-St, respectively. Then, for each model we forecast the one-week-ahead conditional covariance matrix and plug it into the portfolio optimization problem.
